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 A080043 a(n)=floor((2+sqrt(7))^n). 0
 1, 4, 21, 100, 465, 2164, 10053, 46708, 216993, 1008100, 4683381, 21757828, 101081457, 469599316, 2181641637, 10135364500, 47086382913, 218751625156, 1016265649365, 4721317472932, 21934066839825, 101900219778100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. Index entries for linear recurrences with constant coefficients, signature (4, 4, -4, -3). FORMULA G.f.: g(t)=(1+t^2+4t^3)/(1-4t-4t^2+4t^3+3t^4) a(n)=A080042(n)-(1+(-1)^n)/2 a(0)=1, a(1)=4, a(2)=21, a(3)=100, a(n)=4*a(n-1)+4*a(n-2)- 4*a(n-3)- 3*a(n-4). - Harvey P. Dale, Aug 11 2015 MATHEMATICA CoefficientList[Series[(1+t^2+4t^3)/(1-4t-4t^2+4t^3+3t^4), {t, 0, 25}], t] With[{c=2+Sqrt[7]}, Floor[c^Range[0, 30]]] (* or *) LinearRecurrence[{4, 4, -4, -3}, {1, 4, 21, 100}, 30] CROSSREFS Sequence in context: A017967 A292308 A076901 * A240456 A113022 A291184 Adjacent sequences: A080040 A080041 A080042 * A080044 A080045 A080046 KEYWORD easy,nonn AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003 STATUS approved

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Last modified September 8 00:04 EDT 2024. Contains 375749 sequences. (Running on oeis4.)